题目

题型：不详难度：来源：

如图所示，单匝线圈ABCD在外力作用下以速度v向右匀速进入匀强磁场，第二次又以速度2v匀速进入同一匀强磁场．求：

（1）第二次与第一次线圈中最大电流之比；
（2）第二次与第一次外力做功的最大功率之比；
（3）第二次与第一次线圈中产生热量之比．

答案

（1）2∶1 （2）4∶1（3）2∶1  

解析

（1）线圈以速度v匀速进入磁场，当CD边在磁场中时，线框中感应电动势其中L为CD边的长度．                                            
此时线框中的感应电流为，其中R为线框的总电阻．   
同理，线圈以速度2v匀速进入磁场时，线框中的感应电流最大值为
所以第二次与第一次线圈中最大电流之比为2∶1                     （4分）
（2）线圈以速度v匀速进入磁场，当CD边在磁场中时，CD边受安培力最大，最大值为 ．由于线圈做匀速运动，所以此时外力也最大，且外力大小等于安培力大小，此时外力的功率为．                 
同理，线圈以速度2v匀速进入磁场时，外力的最大功率为．
所以第二次与第一次外力做功的最大功率之比为4∶1                   （4分）
（3）线圈以速度v匀速进入磁场，线框中的感应电流为
设AD边长为l，则线框经过时间完全进入磁场，此后线框中不再有感应电流．所以第一次线框中产生的热量为         
同理，线圈以速度2v匀速进入磁场时，线框中产生的热量为                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   
所以第二次与第一次线圈中产生热量之比为2∶1                       （4分）